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# If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x

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Math Expert
Joined: 02 Sep 2009
Posts: 56277
If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 14:22
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Difficulty:

55% (hard)

Question Stats:

55% (01:26) correct 45% (01:14) wrong based on 212 sessions

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GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

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examPAL Representative
Joined: 07 Dec 2017
Posts: 1074
Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 14:57
2
Bunuel wrote:

GMAT Club Tests Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

This is an Alternative approach.

(1) So x^x must equal 1 or -1. This can happen if the exponent is 0 which is impossible by question definition or if x = 1 or if x = -1.
That is, 1^1 = 1 and -1^-1 = -1 so in absolute value both equal 1.
Insufficient.

(2) If we're not sure where to start we'll try easy numbers. If x = 1 then 1^5 = 1^1 = 1 so x = 1 works. If x = 2 then 2^5 = 32 but 2^2 = 4 so x = 2 doesn't work. Since the exponent on the left is 5 it makes sense to try x = 5 which gives 5^5 = 5^5. So x = 1 and x = 5 both work.
Insufficient.

Combined:
x = 1 fits both criteria as shown above. How about x = -1? -1^5 = -1 and -1^-1 = -1. So both x = 1 and x = -1 fit both criteria.
Insufficient.

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Concentration: Entrepreneurship, Finance
Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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20 May 2018, 15:03
1

St1: X=1 or x=-1
St2: x=1 or x=-1

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Math Expert
Joined: 02 Sep 2009
Posts: 56277
Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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24 Dec 2018, 04:10
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

_________________
Intern
Joined: 21 Jan 2018
Posts: 10
Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x  [#permalink]

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03 Jan 2019, 11:25
Bunuel wrote:

GMAT Club Tests' Fresh Question:

If x ≠ 0, what is the value of x ?

(1) $$|x^x| = 1$$

(2) $$x^5 = x^x$$

Hi Bunuel Sir.... Can you let me what is the mistake in my method .
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Re: If x ≠ 0, what is the value of x ? (1) |x^x| = 1 (2) x^5 = x^x   [#permalink] 03 Jan 2019, 11:25
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